| Summary: | There are a wide range of techniques on offer to decision makers choosing between options where each option exhibits a range of attributes. Many of these techniques involve eliciting weights to represent the relative importance of each attribute. This thesis offers a mathematical explanation for the consistent differences in the distribution of weights experienced when a fixed sum method, Point Allocation (PA), and a fixed scale method, Direct Rating (DR), are used. Fixed scale and fixed sum simulations, sampling from the Uniform distribution, produce different weight profiles matching those found in practical applications. Formulae are found representing the distribution of weights produced by the simulations. These enable ranked weights to be calculated, which can be used as surrogates for 'true' weights. In particular, a second major aspect of the study concerns the discovery of a family of piecewise probability density functions to represent the distributions of ranked weights generated using the DR method. The means of the distributions are the Rank Order Distribution (ROD) surrogate weights. These are compared with the Rank Order Centroid (ROC) weights. As the number of attributes in a decision problem increases, the ROD weights approximate to the more easily calculated Rank Sum weights. An interactive survey is conducted, using students and the internet, to compare the PA and DR methods in terms of their ease of use, time taken, accuracy achieved, and user's confidence, in producing weights that represented a series of known "true" weights presented in graphical form. Statistical analysis found significant effects of method, time, accuracy achieved, and confidence of participants, favouring the DR approach. The methods are also compared as a means of obtaining the importance weights given by students to seven listed attributes of universities. A significant difference is found between the pattern of decision weights produced using the two methods confirming previously published studies.
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